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3 years ago

15

Rewrite In simplest radical form x^5/6/x^1/6

1 answer:

Nady [450]3 years ago

3 0

I assume you mean:

[x^(5/6)]/[x^(1/6)]

The rule for dividing similar bases with different exponents is:

(a^b)/(a^c)=a^(b-c)

In this case we have:

x^(5/6-1/6)

x^(4/6)

x^(2/3)

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Vesnalui [34]

- for line B so the set of equations to have no solutions bc. x+y=2 and so y=2-x
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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%2F7%7D%7B7%5Csqrt%7B10%7D%2F2%20%7D" id="TexFormula1" title="\frac{3/7}{7\sqrt{10}

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Multiply the numerator and denominator by 7×2 = 14 to eliminate the denominators of those fractions:

$\dfrac{\dfrac37}{\dfrac{7\sqrt{10}}2}\times\dfrac{14}{14}=\dfrac{3\times2}{7\sqrt{10}\times7}=\dfrac6{49\sqrt{10}}$

Rationalize the denominator by multiplying both numerator and denominator by √10:

$\dfrac6{49\sqrt{10}}\times\dfrac{\sqrt{10}}{\sqrt{10}}=\dfrac{6\sqrt{10}}{49(\sqrt{10})^2}=\dfrac{6\sqrt{10}}{49\times10}=\dfrac{6\sqrt{10}}{490}$

Lastly, cancel the common factor of 2 in both the numerator and denominator (which comes from 6 = 2×3 and 490 = 2×245):

$\dfrac{6\sqrt{10}}{490}=\dfrac{3\sqrt{10}}{245}}$

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